{"id":3952,"date":"2013-10-10T20:19:16","date_gmt":"2013-10-10T18:19:16","guid":{"rendered":"http:\/\/pimedios.es\/?p=3952"},"modified":"2013-10-05T20:39:44","modified_gmt":"2013-10-05T18:39:44","slug":"la-publicacion-de-la-serie-de-grandi","status":"publish","type":"post","link":"https:\/\/pimedios.jesussoto.es\/?p=3952","title":{"rendered":"La publicaci\u00f3n de la serie de Grandi"},"content":{"rendered":"<p><a href=\"http:\/\/upload.wikimedia.org\/wikipedia\/commons\/thumb\/c\/c0\/Guidograndi.jpg\/220px-Guidograndi.jpg\"><img loading=\"lazy\" decoding=\"async\" class=\"alignleft\" alt=\"\" src=\"http:\/\/upload.wikimedia.org\/wikipedia\/commons\/thumb\/c\/c0\/Guidograndi.jpg\/220px-Guidograndi.jpg\" width=\"154\" height=\"205\" \/><\/a>El pasado d\u00eda recib\u00ed un comentario que me trajo al recuerdo <a href=\"http:\/\/pimedios.es\/2010\/01\/19\/la-serie-de-grandi\/\" target=\"_blank\">la serie de Grandi<\/a>. En su momento hable de ella, pero no comente donde Grandi hizo su aportaci\u00f3n.<\/p>\n<p>Pues bien, fue en su peque\u00f1o libro <em>Quadratura circula et hyperbolae per infinitas hyperbolas geometrice exhibita<\/em>,[<a href=\"http:\/\/www.jstor.org\/discover\/10.2307\/2690371?uid=3737952&amp;uid=2&amp;uid=4&amp;sid=21102723436417\" target=\"_blank\">Kline<\/a>] publicado en 1703, cuando obtiene su aportaci\u00f3n a la suma, utilizando la expansi\u00f3n binomial<\/p>\n<p>$$\\frac{1}{1+x}=1-x+x^2-x^3+x^4-x^5+\\ldots,$$<\/p>\n<p>con $x=1$.<\/p>\n","protected":false},"excerpt":{"rendered":"<p>Guido Grandi publica en su peque\u00f1o libro Quadratura circula et hyperbolae per infinitas hyperbolas geometrice exhibita (1703), su aportaci\u00f3n a la suma infinita de 1-1+1-1+1&#8230;, utilizando la expansi\u00f3n binomial.<\/p>\n","protected":false},"author":2,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[6],"tags":[],"class_list":["post-3952","post","type-post","status-publish","format-standard","hentry","category-historia","entry"],"_links":{"self":[{"href":"https:\/\/pimedios.jesussoto.es\/index.php?rest_route=\/wp\/v2\/posts\/3952","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/pimedios.jesussoto.es\/index.php?rest_route=\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/pimedios.jesussoto.es\/index.php?rest_route=\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/pimedios.jesussoto.es\/index.php?rest_route=\/wp\/v2\/users\/2"}],"replies":[{"embeddable":true,"href":"https:\/\/pimedios.jesussoto.es\/index.php?rest_route=%2Fwp%2Fv2%2Fcomments&post=3952"}],"version-history":[{"count":1,"href":"https:\/\/pimedios.jesussoto.es\/index.php?rest_route=\/wp\/v2\/posts\/3952\/revisions"}],"predecessor-version":[{"id":3953,"href":"https:\/\/pimedios.jesussoto.es\/index.php?rest_route=\/wp\/v2\/posts\/3952\/revisions\/3953"}],"wp:attachment":[{"href":"https:\/\/pimedios.jesussoto.es\/index.php?rest_route=%2Fwp%2Fv2%2Fmedia&parent=3952"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/pimedios.jesussoto.es\/index.php?rest_route=%2Fwp%2Fv2%2Fcategories&post=3952"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/pimedios.jesussoto.es\/index.php?rest_route=%2Fwp%2Fv2%2Ftags&post=3952"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}